It depends on your state. There isn't a federal law against it. There are certain restrictions though, which I'll try to explain below.

There is a federal law against possession by civilians (non LEO, non dealer) of machine guns that were not already owned by civilians prior to May 19, 1986.
There is also a $200 tax on the transfer of any machine gun, and you get a "tax stamp" from the US Department of Treasury (eventually) after you file the appropriate paperwork and get that stamp back. Possession without the tax stamp is a federal crime.

(Don't take this as legal advice; I'm just explaining it as I understand it.)

Full auto - machineguns - are legal for normal people to own in, I believe, 37 states. New York is not one of those states. Howsomever, the police and the military are exempt from many laws. That doesn't mean that you, Officer Friendly of the Syracuse Police Department, or you, Sergeant Jones, US Army, can own a machinegun in New York. Means that the Syracuse Police Department can own one, and Officer Friendly, as part of his official duties, could fire it. Means that Sgt. Jones, as part of his official duties in the Army, can shoot that M16.

So it is possible that what you heard was legal full auto use.

Then there are people with fast fingers. My MP40 has a rate of fire of around 650 per minute. That's eleven a second. While I cannot trigger a gun eleven times a second, I can easily do three in a quarter of a second, with a gun I'm used to. Do a couple or three of them and you'd insist I had full auto and was doing three-shot bursts.

There is also something called "bump firing". Best as I can tell (since I have the real deal, I've never felt the need to learn this) you hold the gun loosely. You fire, the gun moves backward in recoil, but because you aren't gripping it tightly it hits your shoulder and bounces forward, where it hits your trigger finger (which is held stiffly). The moving forward against your immobile trigger finger fires the gun again, which makes it bounce backwards and then forward against your finger again. This sounds like full auto, but because the trigger is being tripped each time the gun fires, it isn't. Some people are very good at this.

Then there are cranks which fit many semi rifles such as a semi 1919A4 Browning and allow the shooter to turn the handle, simulating full auto fire. Properly installed and used, they are virtually indistinguishable from a machine gun.